Drill string design methodology for mitigating fatigue failure

ABSTRACT

A drill string design methodology which utilizes a “comparative approach” in the selection of drill string components. The comparative approach in accordance with the present invention can lead to dramatic reductions in fatigue-related problems. In accordance with one aspect of the invention, a method is provided for establishing objective criteria for evaluating individual components of well construction equipment to determine the preferred component or collection of components to be used from the selection of components available. A plurality of quantifiable design parameters relevant to the issues of fatigue damage and failure of drill string components are defined, and an assessment of each of these parameters is made for two or more candidate components being considered for inclusion in the drill string. A comparison is then made between the candidate components&#39; ratings, and a decision to include or exclude a candidate component is made based upon the results of such comparison.

RELATED APPLICATION

[0001] This application claims the priority of prior provisional U.S.patent application Ser. No. 60/464,794, filed on Apr. 23, 2003, whichapplication is hereby incorporated by reference in its entirety.

FIELD OF THE INVENTION

[0002] The present invention relates generally to the field ofhydrocarbon production (i.e., the drilling of oil and gas wells), andmore particularly relates to the design and operation of drill stringsused in such production.

BACKGROUND OF THE INVENTION

[0003] Drill pipe is the principal tool, other than a drilling rig, thatis required for the drilling of an oil or gas well. Its primary purposeis to connect the above-surface drilling rig to the drill bit. Adrilling rig will typically have an inventory of 10,000 to 25,000 feetof drill pipe depending on the size and service requirements of the rig.Joints of drill pipe are connected to each other with a welded-on tooljoint to form what is commonly referred to as the drill string or drillstem.

[0004] When a drilling rig is operating, motors mounted on the rigrotate the drill pipe and drill bit. In addition to connecting thedrilling rig to the drill bit, drill pipe provides a mechanism to steerthe drill bit and serves as a conduit for drilling fluids and cuttings.Drill pipe is a capital good that can be used for the drilling ofmultiple wells. Once a well is completed, the drill pipe may be usedagain in drilling another well until the drill pipe becomes damaged orwears out. It is estimated that the average life of a string of drillpipe is three to five years, depending on usage, and that an average rigwill consume between 125 to 175 joints (3,875 to 5,425 feet) per yearunder normal conditions.

[0005] Drill collars are used in the drilling process to place weight onthe drill bit for better control and penetration. Drill collars aretypically located directly above the drill bit and are typicallymanufactured from a solid steel bar to provide necessary weight.

[0006] So-called “heavy weight drill pipe” or “HWDP” is a thick-walled,preferably seamless tubular product that is less rigid than a drillcollar, but more rigid than standard drill pipe. Those of ordinary skillin the art will appreciate that heavy weight drill pipe can be providedin a drill string to provide a gradual transition zone between theheavier drill collar and the lighter drill pipe. It is generallyrecognized by those of ordinary skill in the art that when heavy weightdrill pipe is not used, the drill pipe near the top of the drill collarsmay be unduly susceptible to fatigue damage and possible failure.Further details regarding the use and characteristics of heavy weightdrill pipe are set forth in U.S. Pat. No. 6,012,744 to Wilson et al.,entitled “Heavy Weight Drill Pipe,” which reference is herebyincorporated by reference herein in its entirety.

[0007] Among the known considerations in the construction of a drillstring is to ensure that it is constructed in a manner which results init remaining intact, functional, and free from leaks during operation.Pump rates, pressure losses, annular velocities, and flow regimes mustaccommodate all drilling requirements, while staying within pressure andflow rate limitations imposed by the hole, the rig pumps, and surfaceequipment. The components in the drill string must enable steering thebit in the desired trajectory, and must accomplish the monitoring andmeasurements required for the hole interval being drilled. Finally, thedrill string should be configured to accomplish operating needs with thelowest possibility of becoming stuck, and to possess the best chance ofrecovery, should it become stuck.

[0008] Those of ordinary skill in the art will appreciate that a drillstring design that meets all needs for structural soundness must alsotake the likely failure mechanisms into account. There are three failuremechanisms that are generally regarded as accounting for a majority allstructural failures: overload, fatigue, and sulfide stress cracking(“SSC”).

[0009] Overload refers to situations in which a component in the drillstring is subjected to loads that exceed its rated capacity.

[0010] Fatigue refers to progressive, localized permanent structuraldamage that occurs when a component undergoes repeated stress cycles,even if such stresses are well below the component's yield strength. Thecyclic stress excursions most often occur when a component is rotatedwhile it is bent or buckled, and by vibration. As the loads on thecomponent cycle up and down, fatigue damage accumulates at high stresspoints in the component, and fatigue cracks form at these points. Suchcracks may grow under continued cyclic loading until failure occurs.

[0011] Finally, sulfide stress cracking is a process in which steel,under tensile stress, cracks in aqueous fluids in the presence ofhydrogen sulfide (H₂S). Several sources of hydrogen sulfide have beenidentified, though the source of principle concern is formation fluids.

[0012] Compared to overload and SSC, fatigue damage and failure is farmore difficult to manage by design. The mechanisms of fatigue are verycomplex. Fatigue is driven by point stress, or the stress in and aroundeach geometric discontinuity, or stress concentrator, on the stringcomponents. The effects of stress concentrators can be very pronounced,and are difficult to evaluate with accuracy. Furthermore, drilling mudcorrosiveness significantly affects fatigue behavior. Finally, sincefatigue damage is cumulative, component history is extremely relevantfor fatigue life prediction, but methods for tracking component historyin meaningful terms are at best gross approximations. (As used herein,the term “fatigue life” will be understood to have its commonlyunderstood meaning in the industry, namely, the amount of time that aparticular component can be reasonably expected to operate underspecified conditions before suffering fatigue failure. Because it is aprediction of future events based only on the available data, which maybe incomplete or imprecise, there is an inherent element of uncertaintyin any quantification of “fatigue life” for any given component.Nevertheless, assuming sufficient, reasonably accurate data isavailable, a quantification of “fatigue life” for a particular componentcan provide a reasonably meaningful indication of probable performanceof that component.)

[0013] Fatigue mechanisms are so complex and the important variables(such as point stress, environment, and history) are so littleunderstood, relatively speaking, that predictive models, on an absolutebasis, have heretofore been found to be of little value. That is, giventhe uncertainty of inputs combined with the complexity of themechanisms, the accuracy of predictive formulas is typically not goodenough to form the basis for design decisions. As a result, there is atendency in the industry not to emphasize fatigue failure mechanisms inthe design and composition of drill strings.

[0014] Currently, the selection of the components used in theconstruction of a well has been dictated by standard practices. Thus, abottomhole assembly or a particular drill string or heavy weight drillpipe string has been specified for a drilling application simply becauseit met an industry practice or standard. The question of whether theparticular drilling component is the best available component for aparticular application is not necessarily addressed in the selectionprocess. A difficulty in specifying the best of the available componentsto be used in the drilling application is that there have been noobjective criteria for evaluating the capabilities of the individualcomponents, particularly as it relates to such components' fatigueresistance.

SUMMARY OF THE INVENTION

[0015] Notwithstanding the limitations of predictive modeling indesigning drill strings that are optimally resistant to fatigue damageand failure, it is nevertheless deemed desirable to achieve drill stringdesigns that are as fatigue resistant as possible. Accordingly, thepresent invention is directed to a drill string design approach whichutilizes a “comparative approach” in the selection of drill stringcomponents. It is believed that the comparative approach in accordancewith the present invention can lead to dramatic reductions infatigue-related problems.

[0016] In accordance with one aspect of the invention, a method isprovided for establishing objective criteria for evaluating individualcomponents of well construction equipment to determine the preferredcomponent or collection of components to be used from the selection ofcomponents available. As used herein, the terms “well construction” and“well construction equipment” are intended to include the procedures andequipment used in the drilling and completion of a well.

[0017] The method of the present invention provides new designconstraints that may be used, for example, by a drilling engineer tomake a selection of drilling equipment for a drill stem to be used indrilling a particular well. As a specific example, an objective of thenew design constraint is to provide a means for a drilling engineer tocompare the fatigue performance of a heavy weight drill string used indrilling a wellbore having a specified wellbore diameter to a standardor to an alternative heavy weight drill string.

[0018] A practical application of the new procedure is that a drillingengineer who has a string of heavy weight drill pipe available as a partof the drilling contractor's equipment can determine whether it is moreefficient to use the available heavy weight drill pipe or to incur theadditional cost of renting a special heavy weight drill pipe string thathas a longer fatigue life in the anticipated application. In some cases,it may be more economical to rent a drill string rather than use thedrill string supplied by the drilling contractor because the fatiguelife of the contractor's heavy weight drill pipe is significantly lessin the anticipated application than that available with a different sizeheavy weight drill pipe string that must be rented from a third party.

[0019] Since a drill string designer almost always performs his or herfunction by selecting from various alternatives, the comparativeapproach in accordance with the presently disclosed embodiment of theinvention involves (1) selecting the design alternative and operatingapproach that provides the lowest stress excursion; (2) selecting thedesign alternative offering the lowest stress concentration; and (3)selecting the design alternative offering the best comparative fatiguelife; and (4) monitoring and reducing corrosion rates in mud systems.

[0020] In accordance with one aspect of the invention, a number ofdesign and operating parameters are quantified as “fatigue indices,” anda predetermined set of design constraints are imposed upon theseindexes.

[0021] In one embodiment, a plurality of quantifiable design parametersrelevant to the issues of fatigue damage and failure of drill stringcomponents are defined, and an assessment of each of these parameters ismade for two or more candidate components being considered for inclusionin the drill string. A comparison is then made between the candidatecomponents' ratings, and a decision to include or exclude a candidatecomponent is made based upon the results of such comparison.

[0022] Among the design parameters defined in accordance with thepresently preferred embodiment of the invention are: “Curvature Index,”“Stability Index,” and “Bending Tolerance Rating.”

[0023] Drill pipe is rotated through dog legs in a process that causesthe pipe to be rotated around a bend. A primary objective of theCurvature Index is to permit comparison of the relative fatigue life ofdrill pipe under different dog legs and tension loadings duringrotation.

[0024] In one embodiment, the Curvature Index (“CI”) gives a measure ofthe relative reduction in fatigue life caused by variations in holecurvature, pipe diameter weight, and grade, and axial tension in thepipe. Using the Curvature Index allows the designer to quantitativelycompare expected fatigue lives at various points in a given string, orbetween alternative design choices in a given hole section. Anotheradvantage of using Curvature Index in drill string design is that it canform the basis for setting inspection frequency and acceptance criteria.

[0025] In a practical application of the use of the Curvature Index, adrilling engineer may have a choice of wellbore trajectories that may beused for reaching a subsurface objective. For example, the trajectorymay involve a wellbore that results in a 3° per 100 ft. dog leg with450,000 lbs tension in the drill string or the wellbore may result in a15° per 100 ft. dog leg with 100,000 lbs tension in the drill string toreach the same objective. Drilling the well with a 3° per 100 ft. dogleg may be less costly than drilling the well with a 15° per 100 ft. dogleg. However, the reduced fatiguedamage done to the drill pipe duringthe drilling of the 15° per 100 ft. dog leg well may offset the savingsassociated with drilling the 3° per 100 ft. dog leg well The StabilityIndex (“SI”) is a measure of the relative fatigue life of bottomholeassemblies (BHAs) that are subjected to being simultaneously buckled androtated. The Stability Index is useful for comparing one designalternative with another to select the alternative most favorable from afatigue standpoint. More specifically it is used to compare variousdrill collar and HWDP sizes run in various hole sizes. Having selected aBHA design, the designer can also use the Stability Index to estimatethe fatigue resistance of the BHA for the purpose of setting inspectionintervals.

[0026] Further in accordance with the present invention, the BendingTolerance Rating (“BTR”) is a rating system useful for rating stresseffects of a collared component or downhole tool based on the maximumstress levels recorded in the drill string, including stressconcentrators.

[0027] The Bending Tolerance Rating is used to assist in the selectionof bottomhole assembly components that may have an unusual or specialconfiguration with structural capabilities and limitations that are notcommonly known to the design engineer. In one embodiment of theinvention, establishing the Bending Tolerance Rating involvesdetermining the most sensitive point on the special purpose bottom holetool by any suitable means such as finite element analysis prediction ofthe tool working in a curve that has a 10  per 100 ft. build. ThisBending Tolerance Rating is useful, for example, when evaluating drillstem components made by companies such as Sperry Sun, Baker, andDyna-Dril. These companies make special purpose bottomhole assemblytools used for “Measurement While Drilling” and “Logging While Drilling”and other specialty subsurface functions. These bottomhole assemblytools have special geometries and structural limitations that are notdefined in the readily available technical literature. For purposes ofdesign analysis, the manufacturers of these specialty tools willdetermine a Bending Tolerance Rating that may be, for example, afunction of the weakest structural point in their special tool. ThisBending Tolerance Rating will be published by the manufacturer and maybe used by the drilling engineer to confirm that the components can beappropriately used in the proposed drill string assembly selected fordrilling a particular wellbore.

BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The foregoing and other features and advantages of the presentinvention will be best understood with reference to a detaileddescription of a preferred embodiment of the invention, which follows,when read in conjunction with the accompanying drawings, wherein:

[0029]FIG. 1 is a flow diagram illustrating a drill string designprocess in accordance with one embodiment of the invention;

[0030]FIG. 2 is a diagram illustrating the fatigue design review step inthe process of FIG. 1;

[0031]FIG. 3 is a graph showing a number of plots of tension versusCurvature Index in accordance with one embodiment of the invention; and

[0032]FIG. 4 is a graph showing a number of plots of hole size versusStability Index in accordance with one embodiment of the invention.

DETAILED DESCRIPTION OF A SPECIFIC EMBODIMENT OF THE INVENTION

[0033] The disclosure that follows, in the interest of clarity, does notdescribe all features of actual implementations of the invention. Itwill be appreciated that in the development of any such actualimplementations, as in any such project, numerous engineering decisionsmust be made to achieve the developers' specific goals and subgoals,which may vary from one implementation to another. Moreover, attentionwill necessarily be paid to proper engineering and practices for theenvironment in question. It will be appreciated that such an effortmight be complex and time-consuming, but would nevertheless be a routineundertaking for those of ordinary skill in the relevant fields.

[0034] Referring to FIG. 1, there is shown a flow diagram of a drillstring design process 10 carried out in accordance with one embodimentof the invention. The first step in the process, represented by block 12in FIG. 1, is to perform an overload structural design. Preferably,overload design is approached from the classical design standpoint. Thatis, the loads are predicted, then components capable of carrying theloads are used. Since the predictive formulas for load calculation aregenerally reliable, the design itself, if properly executed, will bereliable.

[0035] Since the plan for any hole section will have many issues andneeds other than structure, the next step in the drill string designprocess 10 is to optimize the design, as represented by block 14 inFIG. 1. In step 14, the designer must gain maximum leverage over other,non-structural needs, while maintaining a structural design that meetsat least minimum safety factors and design constraints.

[0036] Following steps 12 and 14, in accordance with the presentlydisclosed embodiment of the invention, the next step is to review thedesign to mitigate fatigue attack. This is represented by block 16 inFIG. 1. This step is believed to set the methodology of the presentinvention apart from prior art methodologies, which do not generallytake the fatigue characteristics of drill string components into accountduring the drill string design process. As noted above, it is believedthat this is the case principally due to what is widely viewed as thegeneral unreliability of data which correlate in an absolute sense withthe fatigue characteristics of drill string components.

[0037] In accordance with one aspect of the invention, on the otherhand, the process 16 of reviewing the design for fatigue issues is a“comparative” or relative process. The comparative nature of theapproach is a significant feature of the present invention inasmuch asit tends to overcome the problems associated with the unreliability offatigue mechanism data as an absolute indicator of the fatiguecharacteristics of drill string components.

[0038] Turning to FIG. 2, which illustrates the fatigue design reviewstep 16 from FIG. 1, the fatigue design review approach in accordancewith the presently disclosed embodiment involves comparing alternativedesigns and selecting the design alternative(s) and operating approachesthat (1) provide the lowest stress excursion (block 22 in FIG. 2); (2)provide the lowest stress concentration (block 26 in FIG. 2); (3) offerthe best comparative fatigue life; and (4) reduce corrosion rates (block24 in FIG. 2).

[0039] To facilitate the process of fatigue design review, the presentinvention involves defining one or more “fatigue indices” eachrepresenting a quantification of one or more parameters known tocorrelate to some extent with the fatigue characteristics of the drillstring and its constituent components. As used herein, the term “drillstring component” shall be interpreted broadly to mean any one or moresections or subsection(s) of an overall drill string, including thosesection(s) in the upper drill string and those in the bottomholeassembly. Further, as used herein, the term “fatigue characteristics”shall be understood to mean those characteristics of a drill stringcomponent which either promote or resist fatigue failure. Preferably,each fatigue index is defined such that a fatigue index value ascomputed for a particular drill string component under particularoperating conditions will provide at least a relative measure by whichthe likelihood of fatigue for two or more alternative candidate drillstring components can be compared. By selecting drill string componentsbased on such relative comparisons between alternative candidatecomponents, the drill string designer is advantageously guided towarddefining a drill string which mitigates problems associated with fatiguedamage and failure.

[0040] One such fatigue index is referred to herein as Curvature Index,defined as a measure of the relative reduction in fatigue life caused byrotating a drill pipe tube in a curved hole section, taking into accountthe degree of hole curvature (build/drop rate), pipe size, adjusted pipeweight, grade, and axial tension in the pipe.

[0041] As noted above, in a practical application of the use of theCurvature Index, a drilling engineer may have a choice of wellboretrajectories that may be used for reaching a subsurface objective. Forexample, the trajectory may involve a wellbore that results in a 3° per100 ft. dog leg with 450,000 lbs tension in the drill string or thewellbore may result in a 15° per 100 ft. dog leg with 100,000 lbstension in the drill string to reach the same objective. Drilling thewell with a 3° per 100 ft. dog leg may be less costly than drilling thewell with a 15° per 100 ft. dog leg. However, the reduced fatigue damagedone to the drill pipe during the drilling of the 15° per 100 ft. dogleg well may offset the savings associated with drilling the 3° per 100ft. dog leg well.

[0042] Essentially, the Curvature Index is a non-absolute (i.e.,relative) quantification of the potential for fatigue resulting fromsubjecting a drill string component to curvature and tension in aborehole, which is typically expressed in terms of degrees of curvatureper length of borehole, e.g., 10° per 100 feet. To calculate theCurvature Index for a drill string component, the first step is tocompute the tension on the drill string under analysis. Those ofordinary skill in the art will appreciate that tension is computed basedon various factors, including the weight of the drill string and BHAcomponents, mud volume and/or mud weight, and so on.

[0043] Having determined the tension, which is typically expressed inunits of pounds, the next step in computing the Curvature Index is tocalculate the stress on the drill string. Those of ordinary skill willbe familiar with the many factors taken into account in computing stresson a drill string, among them being the amount of curvature, alsoreferred to as dog-leg severity or DLS to which the drill string issubjected.

[0044] In one embodiment, the stress is computed using the followingmethodology: Consider a drill pipe tube rotating in a dogleg while it'sin tension. The stress in the outer fiber of the drill pipe tube causedby bending (σ_(b)) as it rotates in a dogleg is calculated based in parton the work of Arthur Lubinski. Equations (3) and (4) were obtained fromLubinski's work; however, the forms of these equations were derived tosuit this application. Equation (3) is used to test whether or notcontact is occurring between the drill pipe tube and the hole wall for agiven hole curvature and axial tensile load. Equation (4) is used tocalculate M_(o) for cases in which wall contact does not occur betweenthe drill pipe tube and the hole wall. In the case of wall contact,equation (4) will not apply. Therefore, it was necessary to deriveequation (5) to handle the wall contact case. This derivation wasassisted by the work of Jiang Wu, who solved a similar problem for pipeunder compressive loads. $\begin{matrix}{\sigma_{b} = {\frac{D}{2I}M_{o}}} & (1) \\{{Calculate}\quad c\text{:}} & \quad \\{c = \frac{1}{R_{C}}} & (2) \\{{Calculate}\quad c_{c}\text{:}} & \quad \\{c_{c} = {{\frac{D_{TJ} - D}{L^{2}}\frac{({KL})\quad {\sinh ({KL})}}{2 - {2\quad {\cosh ({KL})}} + {({KL})\quad {\sinh ({KL})}}}} + \frac{w_{b}L^{2}\quad {\sin (\theta)}}{{EI}\quad ({KL})^{2}}}} & (3)\end{matrix}$

[0045] If c is less than c_(c), then the pipe does not contact the holewall and M_(o) is given by equation (4). If c is greater than or equalto c_(c), then the pipe does contact the hole wall and M_(o) is given byequation (5). $\begin{matrix}{M_{o} = {{\frac{KL}{\tanh ({KL})}\lbrack {{EIc} - \frac{w_{b}L^{2}\quad {\sin (\theta)}}{({KL})^{2}}} \rbrack} + \frac{w_{b}L^{2}\quad {\sin (\theta)}}{({KL})^{2}}}} & (4) \\{M_{o} = {\frac{w_{b}L^{2}\quad {\sin (\theta)}}{({KL})^{2}} + {\frac{( {{KL}/2} )}{\tanh \quad ( {{KL}/2} )}\lbrack {{EIc} - \frac{w_{b}L^{2}\quad {\sin (\theta)}}{({KL})^{2}}} \rbrack} +}} & (5) \\{\quad {\frac{{2 \cdot ( {{KL}/2} )^{2}}\quad \tanh \quad ( {{KL}/2} )}{( {{KL}/2} ) - {\tanh \quad ( {{KL}/2} )}}\frac{{EI} \cdot r_{c}}{L^{2}}}} & \quad \\{K = \sqrt{\frac{T}{EI}}} & (6) \\{r_{c} = \frac{D_{TJ} - D}{2}} & (7)\end{matrix}$

[0046] Next, the axial stress (σ_(a)) in the drill pipe tube iscalculated. $\begin{matrix}{\sigma_{a} = \frac{T}{A}} & (8)\end{matrix}$

 A=0.7854(D ² −d ²)  (9)

[0047] Nomenclature for stress calculations:

[0048] A=Drill pipe tube cross sectional area, (in²)

[0049] D=Drill pipe tube outer diameter, (in)

[0050] D_(TJ)=Drill pipe tool joint outer diameter, (in)

[0051] d=Drill pipe tube inner diameter, (in)

[0052] E=Young's modulus, (psi)

[0053] I=Moment of inertia of drill pipe tube, (in⁴)

[0054] L=Half the drill pipe tube length, (in)

[0055] M_(o)=Bending moment on the drill pipe tube at the tool joint,(in-lbs)

[0056] θ=Average inclination angle across the drill pipe tube, (radians)

[0057] T=Axial tensile load, (lbs)

[0058] R_(c)=Radius of curvature of hole wall, (in)

[0059] c=Curvature of hole wall, (in⁻¹)

[0060] c_(c)=Critical curvature of hole wall, (in⁻¹) (hole wallcurvature required for the middle of the drill pipe tube to just contactthe hole wall for a given axial tensile load)

[0061] w_(b)=Buoyed weight per unit length, (lb/in)

[0062] σ_(a)=Axial stress, (psi)

[0063] σ_(b)=Bending stress, (psi)

[0064] The foregoing methodology for computation of stress in the drillstring is derived from the work of Arthur Lubinski, “Maximum PermissibleDog-Legs in Rotary Boreholes,” SPE 1960, revised 1961, which work ishereby incorporated by reference herein. Methodologies for stresscalculation are also discussed in T H Hill Associates, Inc., DS-1, DrillStem Design and Operation, Third edition, January 2003; Hill, T. H.,Ellis, S., Lee, K., Reynolds, N., Zheng, N., “An Innovative DesignApproach to Reduce Drillstring Fatigue,” IADC/SPE 87188, 2004; and JiangWu, “Drill Pipe Bending and Fatigue in Rotary Drilling of HorizontalWells,” SPE 37353, 1996, each of which being hereby incorporated byreference in their entireties. It is believed that those of ordinaryskill in the art will be familiar with still other methodologies forcomputation of stress in drill strings, and the selection and use of aparticular methodology is not believed to be a critical consideration inthe practice of the present invention.

[0065] After computing the stress, which is typically expressed in unitsof pounds per square inch, the next step in computing the Curvatureindex is to compute a “fatigue life” value. In accordance with oneembodiment of the invention, the fatigue life value is determined byassuming that a stress fracture of an arbitrary, predetermined size ispresent in the drill string. Those of ordinary skill in the art willappreciate that the various tools and methods for identifying andlocating stress fractures in drill string components are inherentlylimited, such that stress fractures below a certain size are essentiallyundetectable using conventional techniques. Accordingly, in oneembodiment of the invention, the fatigue life value is computed based onthe assumption that a stress fracture just small enough to beundetectable using conventional techniques is present in the drillstring.

[0066] Based on this assumption, the fatigue life value is computedusing any of various well-known methodologies. In the presentlypreferred embodiment, the well-known Forman Crack Growth Model isapplied. This model is described in further detail in Campbell, J. E.,Gerberich, W. W., and Underwood, J. H., Application of FractureMechanics for Selection of Metallic Structural Materials, ASM, 1982, p.35.

[0067] Summarizing, the Forman Crack Growth Model allows for thecomputation of crack growth rate da/dN (expressed for example, in unitsof inches per stress cycle), as follows:$\frac{a}{N} = \frac{C\quad \Delta \quad K^{n}}{{( {1 - R} )K_{IC}} - {\Delta \quad K}}$

 ΔK=K _(max) −K _(min)

K _(max)=σ_(axial) {square root}{square root over (πa)}F_(axial)+σ_(bending) {square root}{square root over (πa)}F _(bending)

K _(min)=σ_(axial) {square root}{square root over (πa)}F_(axial)−σ_(bending) {square root}{square root over (πa)}F _(bending)

[0068] a=crack depth, (in)

[0069] C=Forman Crack Growth Model empirical coefficient

[0070] da/dN=crack growth rate, (in/cycle)

[0071] F_(axial)=stress intensity geometry and crack shape correctionfactor for axial loads

[0072] F_(bending)=stress intensity geometry and crack shape correctionfactor for bending loads

[0073] K_(IC)=critical stress intensity factor, (ksi {squareroot}{square root over (in)})

[0074] K_(max)=maximum stress intensity factor, (ksi {squareroot}{square root over (in)})

[0075] K_(min)=minimum stress intensity factor, (ksi {squareroot}{square root over (in)})

[0076] n=Forman Crack Growth Model empirical coefficient

[0077] R=ratio of maximum stress to minimum stress

[0078] σ_(axial)=axial stress

[0079] σ_(bending)=bending stress

[0080] Those of ordinary skill in the art will appreciate that the“fatigue life” value is essentially merely a rough estimation ofexpected time to fatigue failure in the drill string component for whichthis value is derived.

[0081] In the presently preferred embodiment of the invention, thefatigue life value is subjected to a predetermined constant multipliervalue to derive the Curvature Index.

[0082] In view of the foregoing, those of ordinary skill in the art willappreciate that deriving the Curvature Index in accordance with thepresently disclosed embodiment involves essentially processing certainknown parameters about the drill string and its environment, based oncertain benchmark assumptions, such as DLS, fracture sizes, and so on.As a consequence, the Curvature Index admits to presentation to drillstring designers in relatively simple formats, making comparison of theCurvature Index for alternative drill string components and/or foralternative wellbore conditions efficient.

[0083]FIG. 3 is one example of how the Curvature Index data may bepresented to a drill string designer. In the graph of FIG. 3, units oftension extend along the horizontal axis, while the Curvature Indexvalues extend along the vertical axis. In the example graph of FIG. 3,each numbered plot (1, 2, 3, . . . 30) corresponds to a differentdog-leg severity (DLS), and the graph of FIG. 3 provides Curvature Indexdata for a particular drill string component (5-inch drill pipe, S135Premium Class, 6{fraction (5/16)}-in tool joint, etc. . . . ). Toutilize the graph of FIG. 3, a drill string designer would need onlyidentify the tension on the drill string and the DLS, and then locatethe intersection of that tension value with the corresponding DLS plot.

[0084] Of course, separate graphs like the exemplary one of FIG. 3 wouldpreferably be provided for different combinations of pipe sizes, pipetypes, tool joint sizes, and so on. With reference to such data, a drillstring designer can make a comparative assessment between alternativedrill string components for a given drilling operation to determine, asbetween any two or more design alternatives, which alternative appearsoptimal from the standpoint of fatigue minimization. It is important tonote that the Curvature Index data is intended to provide onlycomparative information about fatigue resistance as between two or morepossible drill string design alternatives, as opposed to absolute dataabout the fatigue resistance of a particular design.

[0085] Another fatigue index utilized in accordance with the practice ofthe present invention is the Stability Index, which like the CurvatureIndex is a comparative or relative measure of fatigue life of bottomholeassemblies (BHAs), that are simultaneously subjected to buckling androtation. Like the Curvature Index, the Stability Index is useful forcomparing one design from another to select the alternative mostfavorable from a fatigue standpoint. Once the designer has selected abottomhole design, the Stability Index can be used to estimate thefatigue resistance of the BHA for such purposes as setting inspectionintervals and the like.

[0086] Computation of the Stability Index in accordance with thepresently disclosed embodiment of the invention involves steps somewhatsimilar to those involved in computation of the Curvature Index. First,conventional finite element analysis (FEA) techniques are used tocompute the stress in the BHA. Use of FEA techniques for this purpose isvery common in the art, and it is not believed that a detaileddescription of this process is necessary for the purposes of the presentdisclosure.

[0087] Having computed the BHA stress value, a relative “fatigue life”value can be computed using the Forman Crack Growth Model describedabove with reference to the Curvature Index. From the fatigue lifevalue, the Stability Index value can be derived.

[0088] Stability Index data for various alternative BHA configurationscan be presented to and used by a drill string designer in the formshown in the example of FIG. 4. In the graph of FIG. 4, hole size valuesextend along the horizontal axis, and the various plots correspond todifferent sizes of drill collars. For a given hole size and drill collarsize, the Stability Index can be read off of the vertical axis.

[0089] As with the Curvature Index, the Stability Index is intended toprovide comparative or relative data between alternative BHAconfigurations, such that a drill string designer can efficientlycompare, from the standpoint of fatigue failure, the relative merits ofalternative drill string/BHA designs.

[0090] Another comparison factor used in the drill string designmethodology of the present invention is a “Bending Tolerance Rating”.The Bending Tolerance Rating is used to assist in the selection ofbottomhole assembly components that may have an unusual or specialconfiguration with structural capabilities and limitations that are notcommonly known to the design engineer. In a preferred form of theInvention, establishing the Bending Tolerance Rating involvesdetermining the most sensitive point on a special purpose bottom holeassembly tool by any suitable means such as finite element analysisprediction of the tool working in a curve that has a 10° per 100 ft.build. This Bending Tolerance Rating is useful, for example, whenevaluating drill stem components made by companies such as Sperry Sun,Baker, and Dyna-Dril. These companies make special purpose bottomholeassembly tools used for “Measurement While Drilling” and “Logging WhileDrilling” and other specialty subsurface functions. These bottomholeassembly tools have special geometries and structural limitations thatare not defined in the readily available technical literature.

[0091] For purposes of design analysis, the manufacturers of thesespecialty bottom hole assembly tools will determine a Bending ToleranceRating that may be, for example, a function of the weakest structuralpoint in their special tool. This Bending Tolerance Rating can bepublished by the manufacturer and may be used by the drilling engineerto confirm that the components can be appropriately used in the proposeddrill string assembly selected for drilling a particular wellbore.

[0092] The following Table 1 illustrates one example of a BendingTolerance Rating schema in accordance with one embodiment of theinvention. TABLE 1 BTR Maximum Stress in Body (σ_(max)) 1 σ_(max) ≦0.25*MYS 2 0.25*MYS < σ_(max) ≦ 0.4*MYS 3 σ_(max) > 0.4*MYS

[0093] In the example of Table 1, Bending Tolerance Ratings are definedfor various maximum stress ranges as a function of the material yieldstrength (MYS). As a benchmark, finite element analysis can be employedto determine the maximum stress σ_(max) in the body of a tool (includingstress concentrators) for bending in a predetermined dog-leg, forexample, 10° per 100 feet. The BTR for the tool is then read out ofTable 1 based on this maximum stress. In the example of Table 1, a toolwould be assigned a BTR of 1 if FEA shows that the maximum stress in thecurvature is less than or equal to 25% of the tool's material yieldstrength. On the other hand, a tool would be assigned a BTR of 2 if FEAshows that the maximum stress in the curvature is between 25% and 40% ofthe tool's MYS, and a BTR of 3 if the stress is greater than 40% of thetool's MYS. Such a rating system provides a convenient way for drillstring designers to specify to suppliers minimum acceptable bendingtolerances for drill string components.

[0094] The exemplary embodiment of Table 1 above reflects a three-tieredrating system. Those of ordinary skill in the art having the benefit ofthis disclosure will appreciate of course, that rating systems withfewer or more rating levels may be defined in alternative embodiments.

[0095] From the foregoing description, those of ordinary skill in theart will appreciate how the methodology of the present invention may beput into practice in the design of a drill string. First, of course, thedrill string designer must establish one or more operational objectivesin the construction of a wellbore segment, and determining limitingparameters of the wellbore segment to be constructed. These may include,for example, bore size, DLS, pipe type(s) and size(s), and so on.

[0096] Next, the designer determines a selected first working parameterof a plurality of first components of a first type of equipmentavailable to construct the wellbore segment. In the disclosedembodiment, the first working parameter may be curvature or stability.

[0097] The present invention provides a comparison factor for each oftwo or more of the first components, based on the selected workingparameter of the first components. This enables to the designer tocompare the respective comparison factors of the first components, andto select a first component from said plurality of first components,using the comparison of comparison factors, to best meet saidoperational objectives in the construction of the wellbore segment.

[0098] Because at least two different indices may be established forcharacterizing a drillstring component, the methodology of the presentinvention can further involve determining a second working parameter fortwo or more second components selected from a plurality of availablesecond components of a second type of equipment available to constructthe wellbore segment.

[0099] The invention provides a comparison factor for each of said twoor more second components using the second working parameter, enablingthe designer to compare the comparison factors of said secondcomponents, and selecting first and second components, to best meet theoperational objectives, based on comparing the comparison factors.

[0100] From the foregoing, it will be apparent to those of ordinaryskill in the art that a method for constructing a drill string has beendisclosed which adopts a comparative selection process for minimizingthe likelihood of fatigue damage and failure in the resulting drillstring. Although specific embodiments of the invention have beendisclosed, it is to be understood that this has been done solely for thepurposes of describing various aspects of the invention, and is notintended to be limiting with respect to the scope of the invention asdefined by the claims that follow. It is contemplated that varioussubstitutions, alterations, and/or modifications, including but notlimited to those design alternatives specifically mentioned herein, maybe made to the disclosed embodiments without departing from the spiritand scope of the invention as defined in the claims.

What is claimed is:
 1. A method for selecting well constructionequipment, comprising: a. establishing one or more operationalobjectives in the construction of a wellbore segment, b. determininglimiting parameters of the wellbore segment to be constructed, c.determining a selected first working parameter of a plurality of firstcomponents of a first type of equipment available to construct thewellbore segment, d. determining a comparison factor for each of two ormore of the first components, using the selected working parameter ofthe first components, as used in the construction of the wellboresegment, e. comparing the determined comparison factors of the firstcomponents, and f. selecting a first component from said plurality offirst components, using the comparison of comparison factors, to bestmeet said operational objectives in the construction of the wellboresegment.
 2. A method as defined in claim 1, further comprising: a.determining a second working parameter for two or more second componentsselected from a plurality of available second components of a secondtype of equipment available to construct the wellbore segment, b.determining a comparison factor for each of said two or more secondcomponents using the second working parameter, c. comparing comparisonfactors of said second components, and d. selecting first and secondcomponents, to best meet the operational objectives, based on comparingsaid comparison factors.
 3. A method as defined in claim 2, furthercomprising: a. comparing working parameters of assemblies of said firstand second components using the comparison factor established for saidfirst and second components, and b. selecting an assembly of said firstand second components for constructing the wellbore segment using acomparison of comparison factors for assemblies of said first and secondcomponents.
 4. A method as defined in claim 3, further comprising: a.comparing comparison factors of three or more assemblies, each assemblyhaving components of two or more types of equipment, using comparisonfactors established for each type of equipment in said assembly, and b.selecting an assembly of said three or more types of equipment forconstructing the wellbore segment using comparison factors establishedfor said three or more assemblies.
 5. A method as defined in claim 1wherein the operational objective is to minimize the possibility offatigue failure of a drill stem in the construction of a wellboresegment.
 6. A method as defined in claim 1 wherein the operationalobjective is to minimize fatigue-caused damage in a drill stem beingmoved in a curved wellbore section.
 7. A method as defined in claim 6wherein the limiting parameter of the wellbore section is wellborecurvature.
 8. A method as defined in claim 7 wherein said firstcomponents comprises a drillpipe and said limiting parameters includeaxial tension load, stress amplitude (bending stress) and total stressin the pipe.
 9. A method as defined in claim 8 wherein said comparisonfactor for said first components is determined by calculating thefatigue life of the drill pipe and converting the fatigue life into aCurvature Index.
 10. A method as defined in claim 12 wherein saidcomparison factors are reported in graphs of tension load, wellborecurvature, and Curvature Index for various pipe sizes, weights, grades,and classes.
 11. A method as defined in claim 10 wherein said comparisonof comparison factors is performed by using said graphs to comparefatigue damage potential of different combinations of drill pipe typesand sizes, wellbore curvature, and tension load.
 12. A method as definedin claim 1 wherein the objective is to minimize the fatigue inducedfailure of a bottomhole assembly.
 13. A method as defined in claim 12wherein the first components are components of a bottomhole assembly.14. A method as defined in claim 13 wherein said comparison factor isobtained by determining a Stability Index based on the maximum predictedstress exerted on the bottomhole assembly
 15. A method as defined inclaim 14 wherein the Stability Index is a numerical index rangingbetween an infinite life to the shortest life for selected bottomholeassembly components.
 16. A method as defined in claim 1 wherein saidlimiting wellbore condition is a curvature of the wellbore and saidfirst components are downhole tools.
 17. A method as defined in claim 16wherein said comparison factor comprises a bending tolerance ratingdetermined for various maximum stress ranges of the bottomhole tools asa function of material yield strength.
 18. A method as defined in claim17 wherein the bending tolerance rating for said bottomhole tools isreported in a bending tolerance rating table.
 19. A method as defined inclaim 18 wherein said bending tolerance rating table is evaluated toperform said comparison of comparison factors.
 20. A method of designinga drill string comprising a plurality of drill string components,comprising: (a) defining at least one fatigue index quantifyingparameters known to correlate with the fatigue characteristics of adrill string component; (b) identifying at least two alternativecandidate drill string components; (c) computing said fatigue indexvalues for said at least two alternative candidate drill stringcomponents; (d) comparing said computed fatigue index values; (d)selecting one of said at least two alternative candidate drill stringcomponents for inclusion in said drill string based on said comparisonof computed fatigue index values.
 21. A method in accordance with claim20, wherein said at least one fatigue index comprises a Curvature Indexwhich correlates to a prediction of a drill string component's fatiguelife when operated in a curved borehole.
 22. A method in accordance withclaim 20, wherein said at least one fatigue index comprises a StabilityIndex which correlates to a prediction of a drill string component'sfatigue life when simultaneously subjected to buckling and rotation. 23.A method in accordance with claim 20, further comprising: (e)calculating the maximum stress exerted on a drill string component underat least one predetermined set of conditions; and (f) assigning aBending Tolerance Rating to said drill string component based on theratio between said calculated maximum stress and said drill stringcomponent's material yield strength.